Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations

1994 ◽  
Vol 47 (11) ◽  
pp. 545-587 ◽  
Author(s):  
Q.-S. Zheng
Keyword(s):  
Mechanical Behavior ◽  
Constitutive Equations ◽  
Constitutive Laws ◽  
Irreducible Representations ◽  
Two Dimensional ◽  
Applied Mechanics ◽  
Invariant Formulation ◽  
Physical Spaces ◽  
Anisotropic Tensor ◽  
Invariant Approach

Representations in complete and irreducible forms for tensor functions allow general consistent invariant forms of the nonlinear constitutive equations and specify the number and type of the scalar variables involved. They have proved to be even more pertinent in attempts to model mechanical behavior of anisotropic materials, since here invariant conditions predominate and the number and type of independent scalar variables cannot be found by simple arguments. In the last few years, the theory of representations for tensor functions has been well established, including three fundamental principles, a number of essential theorems and a large amount of complete and irreducible representations for both isotropic and anisotropic tensor functions in three- and two-dimensional physical spaces. The objective of the present monograph is to summarize and recapitulate the up-to-date developments and results in the theory of representations for tensor functions for the convenience of further applications in contemporary applied mechanics. Some general topics on unified invariant formulation of constitutive laws are investigated.

Representation of Mechanical Behavior in the Presence of Changing Internal Structure

1988 ◽  
Vol 55 (1) ◽  
pp. 1-10 ◽  
Author(s):  
E. T. Onat ◽  
F. A. Leckie
Keyword(s):  
Mechanical Behavior ◽  
Internal Structure ◽  
Applied Stress ◽  
Constitutive Equations ◽  
Creep Damage ◽  
Main Ideas ◽  
The Relationship ◽  
Small Deformations

The paper is concerned with the representation of the relationship that exists, for a given material and temperature and for small deformations, between histories of applied stress and the observed strain and the accompanying changes in internal structure of the material. Emphasis is given to creep damage in metals as a vehicle for illustration of the main ideas introduced in the paper. In particular, the role played by irreducible even rank tensors in the representation of internal structure is discussed and clarified. The restrictions placed by thermodynamics on constitutive equations are considered and the use of potentials in these equations is examined and criticized.

An Improvement of Multiaxial Ratchetting Modeling Via Yield Surface Distortion

2002 ◽  
Vol 124 (4) ◽  
pp. 402-411 ◽  
Author(s):  
Ludovic Vincent ◽  
Sylvain Calloch ◽  
Tadeusz Kurtyka ◽  
Didier Marquis
Keyword(s):  
Stainless Steel ◽  
Yield Surface ◽  
Constitutive Equations ◽  
316L Stainless Steel ◽  
Constitutive Laws ◽  
Theoretical Studies ◽  
Type 316L ◽  
Polycrystalline Model ◽  
Yield Surface Distortion ◽  
Type 316L Stainless Steel

Many theoretical studies have been made to describe multiaxial ratchetting and most of them have been concentrated on the location of the yield domain, not on its shape. In this paper, we introduce nonlinear kinematic constitutive equations consistent with ratchetting modeling into the distortional model of subsequent yield surfaces proposed by Kurtyka, T., and Zyczkowski, M. We use an efficient polycrystalline model to simulate complex tests including yield surface detections in order to get some reference predictions to use in the development of the constitutive laws introduced into the distortional model. The distortional model is thus qualitatively identified with the polycrystalline model and then quantitatively identified with the experimental results on a type 316L stainless steel. It gives promising results.

Integrated Origami-String System

2019 ◽  
Author(s):  
Ke Liu ◽  
Madelyn Kosednar ◽  
Tomohiro Tachi ◽  
Glaucio H. Paulino
Keyword(s):  
Mechanical Behavior ◽  
Design Space ◽  
Energy Landscape ◽  
Mechanical Systems ◽  
Two Dimensional ◽  
Structural System ◽  
One Dimensional ◽  
Elastic Strings ◽  
Paper Folding

Abstract Origami-inspired mechanical systems are mostly composed of two-dimensional elements, a feature inherited from paper folding. However, do we have to comply with this restriction on our design space? Would it be more approachable to achieve desired performance by integrating elements of different abstract dimensions? In this paper, we propose an integrated structural system consisting of both two-dimensional and one-dimensional elements. We attach elastic strings onto an origami design to modify its mechanical behavior and create new features. We show that, by introducing elastic strings to the recently proposed Morph pattern, we can obtain bistable units with programmable energy landscape. The behavior of this integrated origami-string system can be described by an elegant formulation, which can be used to explore its rich programmability.

Nonlinear Thermodynamics of Moving Material Surfaces in Electric Fields

1988 ◽  
Vol 43 (10) ◽  
pp. 829-846
Author(s):  
H. Wallschlager
Keyword(s):  
Electric Fields ◽  
Physical Meaning ◽  
Constitutive Equations ◽  
Practical Importance ◽  
Two Dimensional ◽  
Boundary Values ◽  
Surface Geometry ◽  
Mechanical Formalism ◽  
Material Surfaces ◽  
Nonlinear Thermodynamics

Abstract A continuum-mechanical formalism is presented for the phenomenological description of moving, curvilinear, material surfaces in electric fields in interaction with volume-phases. In addition to conventional equations (balance and constitutive laws) the explicit use of relations for the surface geometry is introduced. A method to establish nonlinear constitutive equations by tensorial and thermodynamical considerations is proved to be applicable to two-dimensional continua. The resulting equations for boundaries interacting with adjacent volumes are of practical importance for the selfconsistent calculation of boundary values. The physical meaning of the different relations is discussed.

Numerical Simulation for Mechanical Behavior of Carbon Black Filler Particle Reinforced Rubber Matrix Composites

2011 ◽  
Vol 137 ◽  
pp. 1-6
Author(s):  
Qing Li ◽  
Xiao Xiang Yang
Keyword(s):  
Carbon Black ◽  
Mechanical Behavior ◽  
Plane Stress ◽  
Volume Fraction ◽  
Filler Particle ◽  
Three Dimensional ◽  
Rubber Matrix ◽  
Two Dimensional ◽  
Rubber Composites ◽  
Dimensional Plane

In this paper, the micromechanical finite element method based on Representative Volume Element has been applied to study and analyze the macro mechanical properties of the carbon black filled rubber composites by using two-dimensional plane stress simulations and three-dimensional axisymmetric simulations under uniaxial compression respectively. The dependence of the macroscopic stress-strain behavior and the effective elastic modulus of the composites, on particle shape, particle area/volume fraction and particle stiffness has been investigated and discussed. Additionally, the simulation results of the two-dimensional plane stress model and the three-dimensional axisymmetric model are evaluated and compared with the experimental data, which shows that the two-dimensional plane stress simulations generate poor predictions on the mechanical behavior of the carbon black particle reinforced rubber composites, while the three-dimensional axisymmetric simulations appear to give a better prediction.

Comparison of Material Flow Stress Models toward More Realistic Simulations of Friction Stir Processes of Mg AZ31B

2014 ◽  
Vol 783-786 ◽  
pp. 2239-2243 ◽  
Author(s):  
Ali H. Ammouri ◽  
Ramsey F. Hamade
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Constitutive Equations ◽  
Material Model ◽  
The State ◽  
Stir Zone ◽  
State Variables ◽  
Material Models ◽  
Friction Stir ◽  
Comparison Results

Utilizing a proper material model for describing the mechanical behavior of any material is key for a successful simulation of friction stir processing (FSP) where temperature, strain, and strain rate gradients vary abruptly within, and when moving away, from the stirring zone. This work presents a comparison of how faithfully do three different constitutive equations reproduce the state variables of strain, strain rate, and temperature in an FEM simulation of a test-case FSP (1000 rpm spindle speed, and 90 mm/min feed). The three material models considered in this comparison are namely: Johnson-Cook (JC), Sellars-Tegart (ST), and Zerilli-Armstrong (ZA). Constants for these constitutive equations are obtained by fitting these equations to experimental mechanical behavior data collected under a range of strain rates and temperatures of twin-rolled cast wrought AZ31B sheets.It is widely recognized that JC-based models over predicts stress values in the stir zone whereas ST-based models are incapable of capturing work hardening outside of the stir zone. Therefore, a ZA model, being a physical based-HCP specific model, is hereby investigated for its suitability as a material model that would overcome such drawbacks of JC-and ST-based models. The equations from the constitutive models under consideration are fed into an FEM model built using DEFORM 3D to simulate the traverse phases of a friction stir process. Amongst these three material models, comparison results suggest that the HCP-specific ZA model yield better predictions of the state variables: strain, strain rate, and temperature, and, consequently, the estimated values for flow stresses.

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